Shear Wave Velocity Calculator
The shear wave velocity calculator determines the velocity of a shear wave as it moves through a body. This velocity is calculated based on the two main properties of a material, which are its density and its shear modulus. An example of a shear wave is a seismic wave. That's why shear wave velocity is a key parameter in soil analysis in the area of geotechnical evaluation of ground sites. The faster the velocity, the lesser the ground is shaking. Read on to understand what shear wave velocity is and how to calculate it. Pick your unit system — American (Imperial) or Metric (SI) — and the calculator handles the conversions for you.
What is a shear wave?
A shear wave is a type of wave occurring in bulk mediums when the particles oscillate perpendicular to the direction of wave propagation. A shear type of loading causes the shear wave. The shear forces cause a change in the shape of the bulk medium and do not cause any change in the volume of the body. These forces occur in pairs, with either acting along the face of the medium. The shear wave is also known as an S-wave.
We define the shear wave velocity as the square root of the ratio of shear modulus (modulus of rigidity) to the density of material. The velocity of the shear wave Vs in a medium having shear modulus G and density ρ can be written using the shear wave velocity formula:
Vs = √(G / ρ)
The shear wave velocity is about half of the longitudinal wave. The speed of longitudinal waves VL depends on the modulus of elasticity E and density:
VL = √(E / ρ)
How to use the shear wave velocity calculator?
Follow the steps below to find the shear wave velocity:
- Step 1: Enter the shear modulus of the bulk medium (or pick a material from the list to fill it in automatically).
- Step 2: Input the density of the material.
- Step 3: The shear wave velocity calculator will return the answer in m/s, km/s, ft/s, and mph.
Example: What is shear wave velocity in a medium?
Now, let's try an example. Find the shear wave velocity for wave propagation in a copper rod. You can select the material from the list, or enter the shear modulus and density for copper, which are 45 GPa and 8,940 kg/m³, respectively.
- Step 1: Enter the shear modulus, G = 45 GPa.
- Step 2: Input the density of the material, ρ = 8,940 kg/m³.
- Step 3: The calculator will now use the shear wave velocity formula:
Vs = √(G / ρ) = √(45,000,000,000 / 8,940) = 2,243.6 m/s
The velocity of the shear wave in copper is 2.244 km/s.
Shear wave velocity of common materials
These typical values are built into the Material lookup mode. The exact velocity for a specific alloy, grade, or soil can vary with composition, temperature, and processing.
| Material | Shear modulus G (GPa) | Density ρ (kg/m³) | Shear wave velocity Vs (m/s) |
|---|---|---|---|
| Aluminum | 26 | 2,700 | 3,103 |
| Copper | 45 | 8,940 | 2,244 |
| Steel | 79.3 | 7,850 | 3,178 |
| Iron | 82 | 7,870 | 3,228 |
| Gold | 27 | 19,300 | 1,183 |
| Lead | 5.6 | 11,340 | 703 |
| Glass | 26 | 2,500 | 3,225 |
| Titanium | 44 | 4,500 | 3,127 |
| Tungsten | 161 | 19,300 | 2,889 |
Frequently Asked Questions
What is shear wave velocity?
Shear wave velocity (Vs) is the speed at which a shear (S) wave travels through a medium. It equals the square root of the ratio of the material's shear modulus G to its density ρ: Vs = √(G / ρ). A stiffer (higher G) or lighter (lower ρ) material transmits shear waves faster.
How do you calculate shear wave velocity?
Divide the shear modulus G (in pascals) by the density ρ (in kg/m³), then take the square root. For example, copper has G = 45 GPa and ρ = 8,940 kg/m³, so Vs = √(45 × 10⁹ / 8,940) ≈ 2,244 m/s.
Why is shear wave velocity important in geotechnical engineering?
Shear wave velocity is a direct indicator of the stiffness of soil and rock. It is used to classify ground sites for seismic design: the faster the shear wave velocity, the stiffer the ground and the less it shakes during an earthquake.
How does shear wave velocity compare to longitudinal wave velocity?
The shear (S) wave velocity is about half of the longitudinal (P) wave velocity in the same medium. The longitudinal wave velocity is VL = √(E / ρ), where E is the modulus of elasticity, so it is always larger because E > G for ordinary materials.
Does this calculator support American (Imperial) and Metric units?
Yes. Use the Unit System selector to switch between the SI metric system (GPa, kg/m³) and the US customary / Imperial system (psi/ksi, lb/ft³). The result is always shown in m/s, km/s, ft/s, and mph so you can read it in any unit.